Mathematica manipulate
Through the change of what those equations mean or change of the equations themselves the described phenomena would have to change accordingly, assuming that the description of them stays true even if changed or in other words if the equations aren't just changed on paper, but in reality. Physics Manipulation: Most laws of physics are described by mathematical equations.Applied manipulation of mathematics: The ability to manipulate real phenomenons by changing the mathematical rules through which they are described.This means that things like the way reasoning is performed, the mathematical notation, inference rules and which assumptions and models are used when doing math can be changed, but the phenomenons of reality described through the math are unaffected. Abstract manipulation of mathematics: The ability to manipulate mathematics in its abstract form.If instead you fix one of the variables at a desired value, and let the other run, you can see how those settings will affect your equations, overall. Manipulating a plot with two input variables, can be a little confusing if you let both variables change over time.
I'll go ahead and click pause for variable a. If I click pause, after I get back to 100, then you'll see variation for the variable a only and it allows me to see how that would vary with a constant being added of 234.041. If I run them both, then you'll see that I get changes up and down the axis, although it's a little bit hard to follow. As you can see, I have a visualization that includes a linear addition in the range 100 to 1000. I'll click the pause button and now I will display the animation options or animation controls for b, and I'll go ahead and click play for that. So I see the plot changing exactly as it did in the previous movie.
If I want to display the controls for a, I can click it's Show Animation Controls button and I will go ahead and play that. And when I press shift + enter, I see my visualization and I have two different sliders. Now I can close out this list with a right curly bracket and the manipulate keywords argument list with a right square bracket. So I'll type b and we'll have the minimum of 100, comma, 1000 for the maximum. Then a right curly bracket and then a comma, and then a left curly bracket, and that will work with b. So I'll start with a left curly bracket, type the variable a, comma, minus 15, comma, 25. Now type a comma, and I need to define ranges over which I can manipulate the variables a and b. That's the end of the plot commands arguments, so I'll type a right square bracket. So I'll type a comma, then a left curly bracket to start my list, then x, comma, minus six for the minimum, comma, six for the maximum, then a right curly bracket. Now I need to define the range for the x variable, that's in the expression and we'll give the range of the visualization.
#Mathematica manipulate plus#
The last term here was plus a, instead this time, I'm making it plus b, so we can see how two elements work or two manipulable variables. So this is slightly different from the equation I used in the last movie. Minus a, space, x to the second power, plus b. I'll make that x, and it's important that it be a lowercase x. So I'll type, Plot, followed by another left square bracket and the expression that will be visualized within the plot. Now, I need to define what will be manipulated. Then I'll follow that with a left square bracket. I'll start by typing the manipulate keyword. I'm working in a blank Mathematica notebook, so I need to define the expression that I will use to manipulate a visualization.
#Mathematica manipulate how to#
In this movie, I'll show you how to add a second control. In the previous movie, I showed you how to add a single control to manipulate. You can also create an interactive notebook element, that calculates and displays the results that values you or your users input. Entering an expression or equation into Mathematica, let's you calculate a result or visualize data.